With suspense building, high court has more than marriage on the list of big decisions

The justices of the Supreme Court are keeping Americans in suspense as the nation awaits what could be landmark decisions on same-sex marriage and a range of other important issues with just weeks to go in their current session.

The US Supreme Court prepares to enter June with the term's biggest cases yet to be decided. NBC's Pete Williams looks at what's left on the docket.

Can a state limit marriage to the traditional one man-one woman couple, as California did in 2008? Does the U.S. Constitution guarantee same-sex couples a right to marry – a right which supersedes any state law?

And in a second case, the court will decide whether in awarding federal benefits and deciding federal tax policy, the government must recognize the same-sex couples who’ve been married in one of the states that now permit such marriages.

The justices may decide those questions before they conclude their work for the 2012-13 term in the next several weeks. They could find ways to avoid a definitive ruling on each question, but that scenario doesn’t lessen the suspense.

But the marriage decisions are just the high point of a series of marquee cases the court will decide in the coming weeks. Here are the other cases worth watching:

Scope of the Voting Rights Act: Shelby County, Ala., has asked the court to find that Congress exceeded its power when it renewed key sections of the law in 2006.

Under Section 5 of the law, nine states, as well as dozens of counties, cities and elected boards in other states, must seek permission from the Justice Department or a federal court in Washington for any change in voting procedures that they seek to make.

Evan Vucci / AP file photo

House Minority Leader Nancy Pelosi of Calif.,speaks during a rally outside the Supreme Court in Washington, Wednesday, Feb. 27, 2013, before arguments in the Shelby County, Ala., v. Holder voting rights case.

Shelby County contends that the formula used to determine which states are covered by Section 5 is outdated, based on voter turnout and registration data dating from 1972.

But Solicitor General Donald Verrilli said that without Section 5, election officials could cause “great mischief,” by, for example, making changes in polling place locations at the last minute before an election.

If a majority of the justices agree with Shelby County, it will mark a significant change in the way the federal government enforces voting rights.

But a separate section of the Voting Rights Act -- not at issue in this case -- gives the federal government full power to take action against discriminatory voting practices in all 50 states.

Citizenship and voter registration:In another case involving voting, the justices will decide the fate of an Arizona law which requires people to provide proof of American citizenship in order to register to vote.

At issue is whether the 1993 National Voter Registration Act, intended to make voter registration easier, takes precedence over the Arizona law.

Arizona contends that in enacting the citizenship requirement its citizens were responding to legitimate concerns about fraud in voter registration, including some cases in which foreign citizens admitted that they had registered to vote in Arizona.

The pending decision will be significant in marking the limit of what states can do on their own to regulate who registers and who gets to vote.

Racial preferences in university admissions: In a case which will have wide reverberations in colleges and universities across the nation, the high court will decide a challenge brought byAbigail Fisher, an applicant to the University of Texas who was denied admission to the university’s entering class in 2008.

A decision in favor of Fisher would mean that a majority of the court had decided that the time had come to end the experiment in the use of racial preferences in state universities that the high court first approved 35 years ago.

Getting DNA samples from arrestees:Does the Fourth Amendment -- which prohibits "unreasonable searches and seizures" -- allow states to collect and analyze DNA from people arrested and charged with serious crimes –- even if they haven’t yet been convicted?

In 2008, the Maryland legislature required police to collect a DNA sample from anyone arrested for crimes of violence and burglary, or attempts to commit those crimes. Alonzo King, arrested in 2009 for assault, had his DNA sample taken by a cheek swab; that sample was later used to help convict him of a 2003 rape that had gone unsolved.

King challenged that conviction arguing that a DNA cheek swab is a search and is “an intrusion into the person” which is not permitted without a warrant and without “some level of individualized suspicion.”

The Obama administration sided with the state of Maryland in this case. Deputy Solicitor General Michael Dreeben argued before the high court that a DNA sample was justified because “an arrestee is someone whose conduct has given rise to probable cause that he committed a crime, he's in a different position from ordinary citizens.”

The decision in this case will show how the current majority on the court balances individual rights, especially the right to one's own genetic information, against the imperatives of tracking down criminals using all the technologies that science can offer.